**Encryption Factorization**

- Factorization and Pimality Testing, D. M. Bressoud, Undergraduate Texts in Mathematics, Springer-Verlag, 1989.
- Breaking RSA may not be equivalent to factoring, D. Boneh, and R. Venkatesan, Eurocrypt ’98 (LNCS 1233), pp. 59–71, 1998.
- Twenty years of attacks on the RSA cryptosystem, D. Boneh, Notices of the American Mathematical Society (AMS), Vol. 46, No. 2, pp. 203–213, 1999.
- Factorization of RSA-155, RSA News, 1999.
- The future of integer factorization, A. M. Odlyzko, CryptoBytes (The technical newsletter of RSA Laboratories) 1 (no. 2), pp. 5-12, 1995.
- A Survey of Modern Integer Factorization Algorithms, P. L. Montgomery, CWI Quarterly vol. 7 no. 4, pp. 337-365, 1994.
- The NFSNET Project
- The ECMNET Project
- The number field sieve, A. K. Lenstra, H. W. Lenstra, Jr., M. S. Manasse and J. M. Pollard.
- An Implementation of the Number Field Sieve, Marije Elkenbracht-Huizing, Experimental Mathematics, vol. 5 no. 3, pp. 231-253, 1996.
- Faktorisieren mit dem Number Field Sieve(written in German), Jörg Zayer, Ph.D dissertation (Univ. of Saarlandes), 1995.
- Factorization of the tenth Fermat number, R. Brent, Mathematics of Computation vol. 68 no. 225, pp. 429-451, 1999.
- Some Integer Factorization Algorithms using Elliptic Curves, R. Brent, Australian Computer Science Communications vol 8, pp.149-163, 1996.
- ECM Faktorisieren mit elliptischen Kurven(written in German), Franz-Dieter Berger, Diplomarbeit (Univ. of Saarlandes), 1993

**Encryption Discrete Logarithm**

- Discrete logarithms: The past and the future, A. M. Odlyzko, Designs, Codes, and Cryptography 19 , pp. 129-145, 2000.
- The decision Diffie-Hellman problem, D. Boneh, Third ANTS (LNCS 1423), pp. 48–63, 1998.
- Diffie-Hellman, Decision Diffie-Hellman, and Discrete Logarithms, Ueli Maurer and Stefan Wolf, Proceedings of ISIT ’98, IEEE Information Theory Society, p. 327, 1998.
- Computing Discrete Logarithms with the parallelized Kangaroo Method, E. Teske, CACR(U. of Waterloo) Technical Report CORR 2001-01, 2001.
- Square-Root Algorithms for the Discrete Logarithm Problem (A Survey), E. Teske, CACR(U. of Waterloo) Technical Report CORR 2001-07, 2001.
- On the Security of Diffie-Hellman Bits, Maria Isabel Gonzalez Vasco, Igor Shparlinski, Electronic Colloquium on Computational Complexity(ECCC) Report TR00-045, 2000.
- The Relationship Between Breaking the Diffie-Hellman Protocol and Computing Discrete Logarithms, Ueli Maurer and Stefan Wolf, SIAM Journal on Computing, vol. 28, pp. 1689-1721, 1999.
- Generalized Diffie-Hellman modulo a composite is not weaker than factoring, E. Biham, D. Boneh, and O. Reingold, Information Processing Letters (IPL), Vol. 70, pp. 83-87, 1999.
- Hardness of computing the most significant bits of secret keys in Diffie-Hellman and related schemes, D. Boneh, and R. Venkatesan, Crypto ’96 (LNCS 1109), pp. 129–142, 1996.
- Towards the Equivalence of Breaking the Diffie-Hellman Protocol and Computing Discrete Logarithms, Ueli Maurer, CRYPTO ’94 (LNCS 839), pp. 271-281, 1994.
- Computation of discrete logarithms in prime fields, B. A. LaMacchia and A. M. Odlyzko, Designs, Codes, and Cryptography, vol. 1, pp. 46-62. 1991.

**Encryption Elliptic Curve Discrete Logarithm**

- The Arithmetic of Elliptic Curves, J. Silverman, Graduate Texts in Mathematics 106, Springer-Verlag, 1991.
- Remarks on the Security of the Elliptic Curve Cryptosystem, A Certicom Whitepaper, Updated July 2000.
- Faster Attacks on Elliptic Curve Cryptosystems, Michael Wiener and Robert Zuccherato, IEEE P1363: Research Contributions, 1999.
- Overview of elliptic curve cryptography, T. Satoh, K. Araki and S. Miura, PKC’98 (LNCS 1431), pp. 29-49, 1998.
- Elliptic curve public-key cryptosystems – an introduction, E. De Win and B. Preneel, State of the Art in Applied Cryptography (LNCS 1528), pp. 131-141, 1998.
**[related to Hyperelliptic curves]** - Supersingular curves in cryptography, S. Galbraith, Preprint 2000.
- An Algorithm for Solving the Discrete Logarithm on Hyperelliptic Curves, P. Gaudry, Eurocrypt 2000 (LNCS 1807), pp. 19-34, 2000.
- Two Topics in Hyperelliptic Cryptography, Florian Hess, Gadiel Seroussi, and Nigel Smart, HP Labs Technical Reports HPL-2000-118, 2000.
- Computing Discrete Logarithms in High-Genus Hyperelliptic Jacobians in Provably Subexponential Time, A. Enge, CACR(U. of Waterloo) Technical Report CORR 99-04, 1999.
- An Elementary Introduction to Hyperelliptic Curves, A. Menezes, Y. Wu and R. Zuccherato, CACR(U. of Waterloo) Technical Report CORR 96-19, 1996.
**[related to Weil Decent]** - Analysis of the Weil Descent Attack of Gaudry, Hess and Smart, Alfred Menezes & Minghua Qu, CACR(U. of Waterloo) Technical Report CORR 2000-48, 2000.
- Constructive and destructive facets of Weil decent on elliptic curves, P. Gaudry, F. Hess and N. Smart, Preprint 2000.
- A Cryptographic Application of Weil Descent, Nigel P. Smart and Steve Galbraith, HP Labs Technical Reports HPL-1999-70, 1999.
**[related to Xedni Calculus]** - Analysis of the Xedni Calculus Attack, M. Jacobson, N. Koblitz, J. Silverman, A. Stein and E. Teske, CACR(U. of Waterloo) Technical Report CORR 99-06, 1999.
- The Xedni Calculus and the Elliptic Curve Discrete Logarithm Problem, J. Silverman, CACR(U. of Waterloo) Technical Report CORR 99-05, 1999.
- Elliptic curve lifting problem and its applications, H. Kim, J. H. Cheon and S. Hahn, Proc. Japan Academy, Vol. 75(A), pp. 166-169, 1999.
**[related to anomalous curves]** - On the discrete logarithm in the divisor class group of curves, Hans-Georg Rück, Math. Comp., 68, pp. 805-806, 1999.
- Fermat quotients and the polynomial time discrete log algorithm for anomalous elliptic curves, T. Satoh and K. Araki, Commentarii Math. Univ. St. Pauli, vol. 47, pp 81-92, 1998.
- The Discrete Logarithm Problem on Elliptic Curves of Trace One, N. Smart, HP Labs Technical Reports HPL-97-128, 1997.

It is published in Journal of Cryptology, vol. 12 no. 3, pp.193-196, 1999,**[related to supersingular curves]** - Reducing elliptic curve logarithms to logarithms in a finite field, A. Menezes, T. Okamoto and S. Vanstone, IEEE Transactions on Information Theory, vol. 39, pp. 1639-1646, 1993.